Moduli of products of stable varieties. (December 2013)

• Record Type: Journal Article
• Authors: Bhatt, Bhargav; Ho, Wei; Patakfalvi, Zsolt; Schnell, Christian
• Is Part Of: Compositio mathematica. Volume 149:Number 12(2013)
• Page Start: 2036
• Page End: 2070
• Publication Date: 2013-12
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X13007288
• Languages: English
• ISSNs: 0010-437X

Abstract

<abstract abstract-type="normal"> <title>Abstract</title> <p>We study the moduli space of a product of stable varieties over the field of complex numbers, as defined via the minimal model program. Our main results are: (a) taking products gives a well-defined morphism from the product of moduli spaces of stable varieties to the moduli space of a product of stable varieties; (b) this map is always finite étale; and (c) this map very often is an isomorphism. Our results generalize and complete the work of Van Opstall in dimension <inline-formula><alternatives><inline-graphic xlink:href="ark:/27927/pgh1gg8ztj3" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><tex-math><![CDATA[$1$]]></tex-math></alternatives></inline-formula>. The local results rely on a study of the cotangent complex using some derived algebro-geometric methods, while the global ones use some differential-geometric input.</p> </abstract>